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A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics Sebastian Starke Master Thesis Colloquium TAMS, WTM Department of Informatics University of Hamburg 21.06.2016 Master Thesis Page 1 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Contents ● 1. Introduction and Motivation ● 2. Problem Formalization ● 2. Related Work ● 3. Algorithmic Approach ● 4. Experiments and Results ● 5. Conclusion ● 6. Future Work Master Thesis Page 2 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Introduction and Motivation Problem Statement How to adjust a set of joints in order to move an end effector to reach a Cartesian configuration of position and/or orientation? Kinematics „Kinema“ = „Movement / Motion“ → Field of classical mechanics → Motion of rigid bodies by position, velocity, acceleration → No consideration of physical dynamics (mass, force, torque, ...) Master Thesis Page 3 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Introduction and Motivation Applications Robotics → Grasping and Object Manipulation → Bi-Pedal and Multi-Pedal Walking → Human Interaction → Manufacturing Games Industry → Believable characters → Realistic motion → Dynamic and flexible animations Film Industry → Motion Tracking Master Thesis Page 4 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Introduction and Motivation Challenges → Zero up to infinite solutions → Geometric complexity → High dimensionality → Suboptimal extrema and singularities → Joint constraints and types → Solution quality → Accuracy versus Computation Time → Robustness and Reliability → Displacement between solutions → Self-Collision ... Master Thesis Page 5 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Introduction and Motivation (b) (c) (a) (d) (e) Master Thesis Page 6 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Introduction and Motivation Major goals of this thesis A universal IK solver for arbitrary Novel algorithmic improvements kinematic chains for biologically-inspired optimization strategies Real-time capability for Modular extensions applicable interactive frame rates for various problems High accuracy for both Higher adaptivity in exploitation position and orientation and exploration Flexible, few parameters Biologically-plausible and easy-to-use evolutionary concepts Master Thesis Page 7 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Problem Formalization X → Cartesian configuration of position and/or orientation θ → Joint variable configuration Forward Kinematics (FK) Inverse Kinematics (IK) → Straightforward computation → Highly non-trivial → Unique solution → Complexity scales rapidly → Only requires kinematic → Analytical versus Numerical specifications and joint values Master Thesis Page 8 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Problem Formalization Algorithmic Methodology Analytical Numerical Extremely fast and exact Slower computation and only approximative Solution is always found Solution may not always be found Not generally available Applicable to various kinematic models Only derivable for simple and Only requires knowledge specific kinematic geometry of the FK equations Master Thesis Page 9 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Problem Formalization Y → Cartesian target of position and/or orientation μΘ → Weighted joint variable change Numerical IK Update Pose Distance (Rebalanced) Translational Distance Rotational Distance l → Length of the kinematic chain Δ → Distance from base to end effector Master Thesis Page 10 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Related Work → IK researched over decades → Very many different approaches with focus on numerical Jacobian NN CCD IK PSO FABRIK GA Master Thesis Page 11 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Related Work → IK researched over decades → Very many different approaches with focus on numerical Very fast and accurate Jacobian ● Gradient-based (P. Beeson & Repeatable results ● B. Ames – Suffer from suboptimal ● TRAC-IK) extrema CCD NN Produce unrealistic ● (Wang et al.) motion IK PSO FABRIK GA Master Thesis Page 12 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Related Work → IK researched over decades → Very many different approaches with focus on numerical Jacobian NN CCD IK „Forward and Backward ● Reaching IK“ FABRIK Specifically designed for PSO ● (A. Aristidou) character animation and motion tracking Does not operate in joint ● GA space Geometric Predominantly rotational ● movement Master Thesis Page 13 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Related Work → IK researched over decades → Very many different approaches with focus on numerical Jacobian NN CCD IK High scalability ● PSO Parallel search for ● FABRIK (T. Collins & local extrema W. Shen) Flexible design of the ● objective function GA Computationally ● Probabilistic (C. E. González) more expensive Master Thesis Page 14 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Related Work → IK researched over decades → Very many different approaches with focus on numerical Low accuracy ● Learning Struggle with full ● Jacobian posture objectives Only for low degree ● of freedom NN CCD Choice of training ● samples remains very difficult IK PSO FABRIK GA Master Thesis Page 15 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Design Objectives A solution that is existent shall be found. Success The solution shall be as precise as possible. Accuracy → approximately or less than 1mm The solution shall be found as fast as possible. Time → few ms The distance between consecutive solutions shall be Displacement as minimal as possible. The algorithm maintains high robustness, scalability Flexibility and convergency even for greatly varying kinematic structure. Master Thesis Page 16 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Solution Overview Evolutionary Biologically-Inspired Collective Algorithms Optimization Systems + Heuristic Exploitation Master Thesis Page 17 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Genetic Algorithms Particle Swarm Optimization Developed by J. F. Holland Developed by J. Kennedy and R. Eberhart ● ● Inspired by the theory of natural evolution as Inspired by social emerging behaviour of bird flocks ● ● formulated by C. Darwin and schools of fish „Survival of the fittest“ and „Diversity drives change“ ● Rather simple organisms („particles“) collectively ● solve a complex problem Group of individuals within a population that evolves ● over many generations Velocity and direction update according to success ● Selection , Recombination and Mutation of neighbouring particles ● Similarities → Search space exploration by a group of organisms → Solution quality determined by fitness function → Simultaneous search for multiple local extrema → High robustness and scalability as well as effectiveness for multi-objective optimization A.E. Eiben and J. E. Smith – Introduction to Evolutionary Computing , Springer, 2003 D. Floreano and C. Mattiussi – Bio-Inspired Artificial Intelligence, MIT Press, 2008 Master Thesis Page 18 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Genetic Algorithms Particle Swarm Optimization Master Thesis Page 19 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Hybrid Genetic Swarm Algorithm Master Thesis Page 20 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Genotype x → n-dimensional joint variable configuration → Independent of joint types (revolute, prismatic, ...) → Joint limits directly incorporated (clipping) → Allows algebraic vector calculations Master Thesis Page 21 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016

Algorithmic Approach Idea Use randomized weight w for multi-objective optimization → Models dynamic environment → Determines individuals that are „ most responsive to change “ → Biologically plausible Phenotype X → Cartesian configuration obtained by forward kinematics function f π Fitness function measures fitness under evolutionary target Y Ω Master Thesis Page 22 A Hybrid Genetic Swarm Algorithm for Interactive Inverse Kinematics 21.06.2016